Ahf2d Class Reference

Implements a 2D Apparent Horizon Finder. More...

#include <ahf2d_d.h>

Collaboration diagram for Ahf2d:

Public Member Functions
	Ahf2d (int ntheta_in, int nphi_in, double hini_in, double var_in, double fac_in, double err_p_in, double err_e_in, int ahloop_in, Fmv0 *fm_in)
	Constructor for the Ahf2d class.
	~Ahf2d ()
	Destructor for the Ahf2d class. Frees allocated memory.
int	find_ah (double *ah_mass=nullptr, double *ah_spin=nullptr)
	Main function to find the apparent horizon.
void	calc_expansion ()
	Calculates the expansion Theta at all points on the AHF grid.
int	solve_elliptic (double **source, double **solution)
	Solves the elliptic (Poisson-like) equation arising in the iteration.
double	interpolate_to_ah (double ***f, double r, double th, double ph)
	Interpolates a spacetime grid function from the Cartesian grid to a point on the AH surface.
double	calculate_ah_mass ()
	Calculates the irreducible mass of the found horizon.
double	calculate_ah_spin ()
	Calculates the dimensionless spin of the found horizon.
void	print_horizon_shape (const char *filename, double t)
	Prints the current horizon shape h(theta, phi) to a file.
double **	matrix2d (long nrl, long nrh, long ncl, long nch)
	Allocates memory for a 2D AHF grid array.
void	free_matrix2d (double **m, long nrl, long nrh, long ncl, long nch)
	Frees memory allocated by matrix2d().

Public Attributes
int	ntheta
	Number of grid points in theta direction (excluding buffers).
int	nphi
	Number of grid points in phi direction (excluding buffers).
double	dth
	Grid spacing in theta.
double	dphi
	Grid spacing in phi.
double	hini
	Initial guess for the horizon radius (coordinate radius).
double	var
	Acceleration parameter eta for the elliptic solver. Also distinguishes AH/CH.
double	fac
	Mixing factor for updating horizon radius guess during iteration.
double	err_p
	Tolerance for the Poisson solver part.
double	err_e
	Tolerance for the main AH equation solver part.
int	ahloop
	Maximum number of iterations allowed for the solver.
double **	h
	Horizon shape function h(theta, phi).
double **	ths
	Expansion Theta(theta, phi).
Fmv0 *	fm
	Pointer to the Fmv0/Fmv object containing the spacetime grid data.

Protected Member Functions
double	D1th (double **f, int i, int j)
	Calculates the theta derivative of a 2D AHF grid function.
double	D1ph (double **f, int i, int j)
	Calculates the phi derivative of a 2D AHF grid function.

Detailed Description

Implements a 2D Apparent Horizon Finder.

Solves the apparent horizon equation Theta = 0, where Theta is the expansion of outgoing null geodesics, on a spherical coordinate grid. Uses an iterative method involving a Poisson-like solver.

Constructor & Destructor Documentation

Ahf2d()

Ahf2d::Ahf2d	(	int	ntheta_in,
		int	nphi_in,
		double	hini_in,
		double	var_in,
		double	fac_in,
		double	err_p_in,
		double	err_e_in,
		int	ahloop_in,
		Fmv0 *	fm_in )

Constructor for the Ahf2d class.

Parameters

ntheta_in	Number of theta grid points.
nphi_in	Number of phi grid points.
hini_in	Initial guess for horizon radius.
var_in	Solver acceleration parameter eta (etaah).
fac_in	Radius update mixing factor (facn).
err_p_in	Poisson solver tolerance.
err_e_in	AH equation solver tolerance.
ahloop_in	Maximum solver iterations.
fm_in	Pointer to the Fmv0/Fmv object with spacetime data.

~Ahf2d()

Ahf2d::~Ahf2d

(

)

Destructor for the Ahf2d class. Frees allocated memory.

Member Function Documentation

calc_expansion()

void Ahf2d::calc_expansion

(

)

Calculates the expansion Theta at all points on the AHF grid.

Requires interpolating spacetime variables (metric, extrinsic curvature) from the Cartesian grid (fm) to the current guess of the horizon surface defined by h(theta, phi).

calculate_ah_mass()

double Ahf2d::calculate_ah_mass

(

)

Calculates the irreducible mass of the found horizon.

Returns

Irreducible mass M_irr = sqrt(Area / (16 * PI)). Returns -1 if horizon not found.

calculate_ah_spin()

double Ahf2d::calculate_ah_spin

(

)

Calculates the dimensionless spin of the found horizon.

Returns

Dimensionless spin parameter J/M^2. Returns -1 if horizon not found or spin calculation fails.

Note

Spin calculation often requires integrating the extrinsic curvature over the horizon surface.

D1ph()

double Ahf2d::D1ph ( double ** f, int i, int j )

protected

Calculates the phi derivative of a 2D AHF grid function.

D1th()

double Ahf2d::D1th ( double ** f, int i, int j )

protected

Calculates the theta derivative of a 2D AHF grid function.

find_ah()

int Ahf2d::find_ah	(	double *	ah_mass = nullptr,
		double *	ah_spin = nullptr )

Main function to find the apparent horizon.

Iteratively solves for the horizon shape function h(theta, phi) until the expansion Theta is sufficiently close to zero or the maximum number of iterations is reached.

Parameters

[out]	ah_mass	Pointer to store the calculated irreducible mass (optional).
[out]	ah_spin	Pointer to store the calculated dimensionless spin (optional).

Returns

0 on success, non-zero on failure (e.g., no convergence).

Here is the caller graph for this function:

free_matrix2d()

void Ahf2d::free_matrix2d	(	double **	m,
		long	nrl,
		long	nrh,
		long	ncl,
		long	nch )

Frees memory allocated by matrix2d().

interpolate_to_ah()

double Ahf2d::interpolate_to_ah	(	double ***	f,
		double	r,
		double	th,
		double	ph )

Interpolates a spacetime grid function from the Cartesian grid to a point on the AH surface.

Parameters

f	Pointer to the 3D Cartesian grid function data (e.g., fm->alp).
r	Coordinate radius of the point.
th	Theta angle of the point.
ph	Phi angle of the point.

Returns

Interpolated value of f at (r, th, ph).

Note

Needs careful implementation of coordinate transformation and interpolation (e.g., trilinear).

matrix2d()

double ** Ahf2d::matrix2d	(	long	nrl,
		long	nrh,
		long	ncl,
		long	nch )

Allocates memory for a 2D AHF grid array.

print_horizon_shape()

void Ahf2d::print_horizon_shape	(	const char *	filename,
		double	t )

Prints the current horizon shape h(theta, phi) to a file.

Parameters

filename	Name of the output file.
t	Current simulation time to include in the output.

solve_elliptic()

int Ahf2d::solve_elliptic	(	double **	source,
		double **	solution )

Solves the elliptic (Poisson-like) equation arising in the iteration.

This is likely the core iterative solver step (e.g., SOR, CG).

Parameters

[in]	source	The source term for the elliptic equation (related to Theta).
[out]	solution	The solution array (update to h or correction).

Returns

Number of iterations taken, or -1 on failure.

Member Data Documentation

ahloop

int Ahf2d::ahloop

Maximum number of iterations allowed for the solver.

dphi

double Ahf2d::dphi

Grid spacing in phi.

dth

double Ahf2d::dth

Grid spacing in theta.

err_e

double Ahf2d::err_e

Tolerance for the main AH equation solver part.

err_p

double Ahf2d::err_p

Tolerance for the Poisson solver part.

fac

double Ahf2d::fac

Mixing factor for updating horizon radius guess during iteration.

fm

Fmv0* Ahf2d::fm

Pointer to the Fmv0/Fmv object containing the spacetime grid data.

h

double** Ahf2d::h

Horizon shape function h(theta, phi).

hini

double Ahf2d::hini

Initial guess for the horizon radius (coordinate radius).

nphi

int Ahf2d::nphi

Number of grid points in phi direction (excluding buffers).

ntheta

int Ahf2d::ntheta

Number of grid points in theta direction (excluding buffers).

ths

double** Ahf2d::ths

Expansion Theta(theta, phi).

var

double Ahf2d::var

Acceleration parameter eta for the elliptic solver. Also distinguishes AH/CH.

---

The documentation for this class was generated from the following file:

• ahf2d_d.h